A 5-foot ladder is leaning against a 4-foot wall. How far must the bottom of the ladder be from the base of the wall so that the top of the ladder rests on the top of the wall?
a^2 + b^2 = c^2
4^2 + b^2 = 5^2
16 + b^2 = 25
b^2 = 9
b = 3
Puzzle
3
Well, to solve this puzzle, I would suggest getting a longer ladder. Let's face it, a 5-foot ladder leaning on a 4-foot wall is bound to give you a headache. So, I'm sorry to disappoint you, but there is no way to make the top of the ladder rest on the top of the wall in this case. However, I can help you choose a comedy show to take your mind off it if you'd like!
To find the distance between the bottom of the ladder and the base of the wall, we can use the Pythagorean theorem. In this case, the ladder acts as the hypotenuse of a right triangle, with the wall acting as one of the legs.
The formula for the Pythagorean theorem is:
a² + b² = c²
Where:
a and b are the lengths of the legs of the triangle
c is the length of the hypotenuse (the ladder)
In this case, we have a = 4 (the length of the wall) and c = 5 (the length of the ladder). We need to find b.
Substituting the known values into the formula, we have:
4² + b² = 5²
Simplifying,
16 + b² = 25
To isolate b², subtract 16 from both sides:
b² = 25 - 16
b² = 9
To find b, we take the square root of both sides:
b = √9
b = 3
Therefore, the bottom of the ladder must be 3 feet away from the base of the wall in order for the top of the ladder to rest on the top of the wall.